@article{SIGMA_2016_12_a66,
author = {Salvatore Stella and Pavel Tumarkin},
title = {Exchange {Relations} for {Finite} {Type} {Cluster} {Algebras} with {Acyclic} {Initial} {Seed} and {Principal} {Coefficients}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2016},
volume = {12},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a66/}
}
TY - JOUR AU - Salvatore Stella AU - Pavel Tumarkin TI - Exchange Relations for Finite Type Cluster Algebras with Acyclic Initial Seed and Principal Coefficients JO - Symmetry, integrability and geometry: methods and applications PY - 2016 VL - 12 UR - http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a66/ LA - en ID - SIGMA_2016_12_a66 ER -
%0 Journal Article %A Salvatore Stella %A Pavel Tumarkin %T Exchange Relations for Finite Type Cluster Algebras with Acyclic Initial Seed and Principal Coefficients %J Symmetry, integrability and geometry: methods and applications %D 2016 %V 12 %U http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a66/ %G en %F SIGMA_2016_12_a66
Salvatore Stella; Pavel Tumarkin. Exchange Relations for Finite Type Cluster Algebras with Acyclic Initial Seed and Principal Coefficients. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a66/
[1] Caldero P., Keller B., “From triangulated categories to cluster algebras”, Invent. Math., 172 (2008), 169–211, arXiv: math.RT/0506018 | DOI | MR | Zbl
[2] Chapoton F., Fomin S., Zelevinsky A., “Polytopal realizations of generalized associahedra”, Canad. Math. Bull., 45 (2002), 537–566, arXiv: math.CO/0202004 | DOI | MR | Zbl
[3] Felikson A., Shapiro M., Tumarkin P., “Cluster algebras and triangulated orbifolds”, Adv. Math., 231 (2012), 2953–3002, arXiv: 1111.3449 | DOI | MR | Zbl
[4] Felikson A., Tumarkin P., Bases for cluster algebras from orbifolds, arXiv: 1511.08023
[5] Fomin S., Shapiro M., Thurston D., “Cluster algebras and triangulated surfaces. I. Cluster complexes”, Acta Math., 201 (2008), 83–146, arXiv: math.RA/0608367 | DOI | MR | Zbl
[6] Fomin S., Thurston D., Cluster algebras and triangulated surfaces. II. Lambda lengths, arXiv: 1210.5569
[7] Fomin S., Zelevinsky A., “Cluster algebras. I. Foundations”, J. Amer. Math. Soc., 15 (2002), 497–529, arXiv: math.RT/0104151 | DOI | MR | Zbl
[8] Fomin S., Zelevinsky A., “Cluster algebras. II. Finite type classification”, Invent. Math., 154 (2003), 63–121, arXiv: math.RA/0208229 | DOI | MR | Zbl
[9] Fomin S., Zelevinsky A., “Cluster algebras. IV. Coefficients”, Compos. Math., 143 (2007), 112–164, arXiv: math.RA/0602259 | DOI | MR | Zbl
[10] Musiker G., Williams L., “Matrix formulae and skein relations for cluster algebras from surfaces”, Int. Math. Res. Not., 2013 (2013), 2891–2944, arXiv: 1108.3382 | DOI | MR | Zbl
[11] Nakanishi T., Stella S., “Diagrammatic description of $c$-vectors and $d$-vectors of cluster algebras of finite type”, Electron. J. Combin., 21 (2014), 1.3, 107, arXiv: 1210.6299 | MR | Zbl
[12] Nakanishi T., Zelevinsky A., “On tropical dualities in cluster algebras”, Algebraic Groups and Quantum Groups, Contemp. Math., 565, Amer. Math. Soc., Providence, RI, 2012, 217–226, arXiv: 1101.3736 | DOI | MR | Zbl
[13] Reading N., “Universal geometric cluster algebras from surfaces”, Trans. Amer. Math. Soc., 366 (2014), 6647–6685, arXiv: 1209.4095 | DOI | MR | Zbl
[14] Schiffler R., “A geometric model for cluster categories of type $D_n$”, J. Algebraic Combin., 27 (2008), 1–21, arXiv: math.RT/0608264 | DOI | MR | Zbl
[15] Stella S., “Polyhedral models for generalized associahedra via Coxeter elements”, J. Algebraic Combin., 38 (2013), 121–158, arXiv: 1111.1657 | DOI | MR | Zbl
[16] Yang S.-W., Zelevinsky A., “Cluster algebras of finite type via Coxeter elements and principal minors”, Transform. Groups, 13 (2008), 855–895, arXiv: 0804.3303 | DOI | MR | Zbl